JP7408246B2 - Dissipation tangent measurement method and measurement jig - Google Patents

Description

The present invention relates to a dielectric loss tangent measurement method for measuring the dielectric loss tangent of a liquid substance, and a measurement jig used in the dielectric loss tangent measurement method.

The configuration of a conventional measurement method for measuring dielectric loss tangent is shown in FIG. The conventional method for measuring dielectric loss tangent shown in FIG. 13 is a capacitance method 100 using parallel electrodes. They are sandwiched to form a capacitor. Then, a voltage of a predetermined frequency is applied from the voltage source 110 to the formed capacitor to obtain the electrical characteristics of the capacitor. Next, the obtained electrical characteristics are analyzed to calculate the dielectric loss tangent of the dielectric 120. In this capacitive method 100, the effective area and shape of the electrodes 111 and 112 have a large influence on the measurement of the dielectric loss tangent, making it difficult to obtain high measurement accuracy. Furthermore, since the structure is such that no liquid can be sandwiched between the electrodes 111 and 112, a liquid substance cannot be used as the dielectric 120, and the dielectric loss tangent of the liquid substance cannot be measured.

A conventional measuring method capable of measuring the dielectric loss tangent of a liquid substance is disclosed in Non-Patent Document 1. The conventional measurement method disclosed in Non-Patent Document 1 is a measurement method for measuring the complex dielectric constant of liquid crystal using a coaxial line that can be filled with liquid. The configuration of a coaxial line in this conventional measurement method is shown in FIGS. 14(a) and 14(b). FIG. 14(a) is a front view showing the structure of the coaxial line 200 in cross section, and FIG. 14(b) is a side view showing the structure of the coaxial line 200 in cross section.
The coaxial line 200 shown in these figures consists of a cylindrical outer conductor 210 made of metal, and a conductive center conductor 211 disposed at the center of a through hole formed in the axial direction in the outer conductor 210. It is configured. A connector 212 having a coaxial structure is provided at one end of the coaxial line 200, and a connector 213 having a coaxial structure is also provided at the other end. The inside of the through hole, which has a coaxial structure, is divided into three parts in the axial direction, and the area on the connector 212 side is sealed with an insulating sealing material 215, and the area on the connector 213 side is also sealed with an insulating sealing material 215. It is sealed. The area between the two sealants 215 is a filling area in which liquid 220, which is a sample, is filled, and the liquid 220 is filled into the filling area through the hole into which the screw 214 is screwed. Once the filling area is filled with liquid 220, the screw 214 is screwed into the hole to seal the filling area.

The filling area is filled with liquid crystal as the liquid 220, the connector 212 is used as an input terminal, the connector 213 is used as an output terminal, and a signal of a predetermined frequency is applied from the connector 212 to measure the S parameter. Then, the dielectric loss tangent of the liquid crystal can be calculated based on the transmission amount and phase amount of S21 of the S parameter. In this case, the dielectric constant of the sealant 215 is known.

Tohoku University Telecommunication Research Institute Engineering Research Group Transmission Engineering Research Group Transmission Engineering Research Group Materials Vol. 2018, No. 601-4, September 2018 Shinji Abe and 5 other authors “Measurement of complex dielectric constant of liquid crystal using liquid-filled coaxial line” P. 1-5

With conventional measurement methods, it is possible to measure the dielectric loss tangent of liquid substances, but as the frequency increases, it becomes difficult to measure the dielectric loss tangent, making it difficult to measure the dielectric loss tangent over a wide band. .
SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a dielectric loss tangent measurement method capable of measuring the dielectric loss tangent of a liquid substance over a wide band, and a measurement jig used in the dielectric loss tangent measurement method.

In order to achieve the above object, the dielectric loss tangent measurement method of the present invention consists of an outer conductor and a center conductor placed at the center of the outer conductor, and has a length L that can fill the inside with a sample liquid. A dielectric loss tangent measurement method using a measurement jig comprising a coaxial line, an input connector provided at one end of the coaxial line, and an output connector provided at the other end of the coaxial line, the method comprising: The impedance of the output connector is Zo, and when a signal of a predetermined measurement frequency is input to the input connector, Fo is the frequency at which the phase amount of the coaxial line without liquid is 180 degrees, and Fo is the frequency when the coaxial line is filled with liquid. When the frequency at which the phase amount of the coaxial line in the state of The most important feature is to calculate at least the dielectric loss tangent of the liquid at an integer of .
In the dielectric loss tangent measuring method of the present invention, a hole portion capable of filling the liquid is provided in the coaxial line between the input connector and the coaxial line and between the output connector and the coaxial line. A flange is provided, and after the coaxial line is filled with the liquid through the hole, a screw is screwed into the hole to seal the hole.
Further, in the dielectric loss tangent measurement method of the present invention, when n is a positive integer of 1 or more, the dielectric loss tangent tan δ of the liquid at nFs is:
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) }
It can be calculated as follows.
Furthermore, in the dielectric loss tangent measurement method of the present invention, in addition to calculating the dielectric loss tangent of the liquid based on the insertion loss IL, Fo, Fs, and the length L of the measurement jig, nFs(n is a positive integer of 1 or more), the dielectric constant of the liquid can also be calculated.

In order to achieve the above object, the measuring jig of the present invention consists of an outer conductor and a center conductor placed at the center of the outer conductor, and has a coaxial length L that can be filled with a sample liquid. a line, an input connector provided at one end of the coaxial line, and an output connector provided at the other end of the coaxial line, and with the impedance of the input connector and the output connector being Zo, the input connector is provided with a predetermined impedance. Fo is the frequency at which the phase amount of the coaxial line without liquid is 180° when a signal of the measurement frequency is input, and the frequency at which the phase amount of the coaxial line in the liquid-filled state is 180° is Fo. When is Fs, at least the dielectric loss tangent of the liquid at nFs (n is a positive integer of 1 or more) can be calculated based on the insertion loss IL, Fo, Fs, and the length L of the measurement jig. This is the most important feature.
In the measurement jig of the present invention, a flange is provided with a hole that can fill the liquid into the coaxial line between the input connector and the coaxial line and between the output connector and the coaxial line. is provided, and after filling the coaxial line with the asthma liquid through the hole, a screw is screwed into the hole to seal the hole.
Further, in the measurement jig of the present invention, when n is a positive integer of 1 or more, the dielectric loss tangent tan δ of the liquid at nFs is:
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) }
It can be calculated as follows.
Furthermore, in the measuring jig of the present invention, in addition to being able to calculate the dielectric loss tangent of the liquid based on the insertion loss IL, Fo, Fs, and the length L of the measuring jig, nFs (n is 1 The relative dielectric constant of the liquid at the above positive integer) can also be calculated.

The dielectric loss tangent measurement method of the present invention uses a measurement jig equipped with a coaxial line having a length L that can be filled with a sample liquid, and the phase amount of the coaxial line without being filled with liquid is 180°. The dielectric loss tangent tan δ of the liquid at nFs can be calculated based on the frequency Fo and the frequency Fs at which the phase amount of the coaxial line filled with liquid is 180°. As a result, the dielectric loss tangent measurement method and the measurement jig used for the dielectric loss tangent measurement method of the present invention can measure at least the dielectric loss tangent of the liquid substance even if the frequency becomes high.

1 is a front view and a side view showing the configuration of a measuring jig according to an embodiment of the present invention. FIG. 1 is a partially sectional front view showing the configuration of a measuring jig according to an embodiment of the present invention; FIG. FIG. 2 is a circuit diagram showing the electrical configuration of a coaxial line. FIG. 2 is a circuit diagram showing a configuration that provides dielectric loss to a coaxial line. FIG. 2 is a circuit diagram showing an equivalent circuit that causes dielectric loss to a coaxial line. FIG. 3 is a circuit diagram showing an equivalent circuit of a coaxial line. It is a figure which shows the frequency characteristic of return loss and insertion loss when the measuring jig of the Example of this invention is filled with liquid. 1 is a chart showing the results of measurement by the dielectric loss tangent measuring method of the present invention using the measurement jig of the example of the present invention. It is a chart showing other results measured by the dielectric loss tangent measuring method of the present invention using the measuring jig of the example of the present invention. It is a chart showing still other results measured by the dielectric loss tangent measuring method of the present invention using the measuring jig of the example of the present invention. It is a figure which shows the frequency characteristic of return loss and insertion loss when the measuring jig of the Example of this invention is filled with another liquid. FIG. 7 is a diagram showing the frequency characteristics of the dielectric loss tangent when the measurement jig according to the embodiment of the present invention is filled with another liquid. FIG. 2 is a circuit diagram showing a conventional method for measuring dielectric loss tangent. FIG. 2 is a front view and a side view showing, in cross-sectional view, the configuration of a coaxial line used in a conventional measurement method capable of measuring the dielectric loss tangent of a liquid substance.

<Example of measurement jig of the present invention>
The dielectric loss tangent measuring method of measuring the dielectric loss tangent of a liquid substance of the present invention uses a measuring jig according to an embodiment of the present invention, and the measuring jig according to an embodiment of the present invention will be described. The configuration of a measuring jig 1 according to an embodiment of the present invention is shown in FIGS. 1(a) and 2(b) and FIG. 1(a) is a front view showing the configuration of the measurement jig 1, FIG. 1(b) is a side view showing the configuration of the measurement jig 1, and FIG. 2 shows a part of the configuration of the measurement jig 1. It is a front view shown in a sectional view.
The measuring jig 1 according to the embodiment of the present invention shown in these figures includes a cylindrical outer conductor 12 made of conductive material such as metal, and a cylindrical outer conductor 12 made of metal or the like placed at the center of the outer conductor 12 in the axial direction. It has a coaxial line consisting of a conductive center conductor 14, and a conductive outer conductor flange 12a made of a disc-shaped metal or the like having a predetermined thickness is fixed to one end of the outer conductor 12. A conductive outer conductor flange 12b made of metal or the like and having a predetermined thickness is fixed to the other end of the outer conductor 12. The outer conductor flange 12a and the outer conductor flange 12b have a line-symmetrical shape, and a through hole having a diameter equal to the inner diameter of the outer conductor 12 is formed in the center. Further, an injection hole 12c is formed on the side circumferential surface of the outer conductor flange 12a, and an injection hole 12c is formed through which a sample liquid can be injected into the coaxial line, and an injection hole 12c is formed on the side circumferential surface of the outer conductor flange 12b. An injection hole 12d through which liquid can be injected into the coaxial line is similarly formed. The liquid injected from the injection hole 12c or 12d fills the space between the center conductor 14 and the outer conductor 12. Screw means for sealing can be screwed into the injection holes 12c and 12d.

An electrically conductive connector flange 11a made of a disc-shaped metal or the like has an input connector 11 having a coaxial structure attached to the outer circular surface of the outer conductor flange 12a with four screws. It is fixed by four screws 11b arranged at equal intervals. An O-ring 12e is sandwiched between the surfaces where the outer conductor flange 12a and the connector flange 11a meet to form a watertight structure. It is engaged within a circular recess formed in the surface. Note that the tip of the center pin of the input connector 11 is inserted into a hole formed in one end of the center conductor 14, and the center pin is connected to one end of the center conductor 14.
Further, an output connector 13 having a coaxial structure is attached to the outer circular surface of the outer conductor flange 12b with four screws, and a connector flange 13a made of conductive metal or the like has a disc shape. are fixed by four screws 13b arranged at equal intervals. An O-ring 12f is sandwiched between the surfaces where the outer conductor flange 12b and the connector flange 13a meet to form a watertight structure. It is engaged within a circular recess formed in the surface. Note that the tip of the center pin in the output connector 13 is inserted into a hole formed at the other end of the center conductor 14, and the center pin is connected to the other end of the center conductor 14.

<Dielectric loss tangent measurement method of the present invention>
The dielectric loss tangent measuring method of the present invention will be described in which the dielectric loss tangent of a liquid substance is measured using the measuring jig 1 according to the present invention shown in FIGS. 1 and 2.
Here, the impedance of the input connector 11 and the output connector 13 is set to Zo, and the outer part of the center conductor 14 is The diameter a and the inner diameter b of the outer conductor 12 are set. As a result, the coaxial line in the measurement jig 1 is accurately aligned with Zo over its entire length, and also functions as a connection connector. Then, the input connector 11 is connected to the first port of the network analyzer, the output connector 13 is connected to the second port of the network analyzer, and calibration work is performed. In the calibration work, the first port, which is the signal output port, and the second port, which is the signal input port, are calibrated to open, short, and terminate, and both ports are matched to the impedance Zo, and the return loss RL (S11 , S22) is set to -∞dB. Subsequently, a through calibration in which both ports are directly connected is performed using the measurement jig 1 that is not filled with liquid. Through this work, the insertion loss including the measurement jig 1 is added to the insertion loss IL (S parameters of S21 and S12), and the insertion loss IL between the first port and the second port is standardized to 0 dB. become. As a result, changes in the return loss RL and insertion loss IL after the liquid is injected into the measurement jig 1 according to the present invention can be identified as being due to the action of the liquid injected into the measurement jig 1.

Therefore, a liquid to be used as a sample is injected through the injection holes 12c and 12d of the measurement jig 1, and the injection holes 12c and 12d are sealed by screw means. The liquid injected from the injection hole 12d fills the coaxial line consisting of the center conductor 14 and the outer conductor 12, and specifically, the liquid fills the space between the center conductor 14 and the outer conductor 12. When a liquid such as liquid crystal is filled into the coaxial line through the injection hole 12c, the dielectric loss tangent of the liquid crystal can be measured. Next, a signal of a predetermined frequency is input to the input terminal 11 of the measurement jig 1, and the frequency characteristics of the insertion loss IL and the frequency characteristics of the return loss RL in the measurement jig 1 are measured by a network analyzer. Next, when n is a positive integer of 1 or more, based on the measurement results, determine the frequency nFs at which the phase of the coaxial line consisting of the center conductor 14 and the outer conductor 12 is n times 180°, and the frequency nFs at that time. Find the insertion loss IL. Thereby, the dielectric loss tangent tan δ of the liquid filled in the coaxial line can be determined from the following equation (1).
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) } (1)
However, in equation (1), L is the length of the coaxial line filled with liquid, and Fo is the frequency at which the phase becomes 180° in the coaxial line when the coaxial line is not filled with liquid. In this case, the frequency at which the phase of the coaxial line is n times 180° is nFo. Note that the unit of L is m (meter), the unit of IL is dB, and the unit of Fo and Fs is MHz.

<Details of dielectric loss tangent measurement method>
It will be explained below that the dielectric loss tangent tan δ can be determined by the above equation (1).
Figure 3 shows a circuit diagram of a typical coaxial line. In FIG. 3, the coaxial length of the lossless coaxial line 20 is L, its phase is θ, and the characteristic impedance is W. The outer conductor of the lossless coaxial line 20 is grounded, one end of the center conductor of the lossless coaxial line 20 is connected to the input terminal Pin, the other end of the center conductor is connected to the output terminal Pout, and the impedance of Pin and Pout is Let's say Zo.
When the insulator between the outer conductor and the center conductor of the lossless coaxial line 20 is air, the dielectric constant εr of the insulator becomes approximately 1, and the wavelength is not shortened substantially. In this case, where Fo is the frequency at which the phase of the lossless coaxial line 20 is 180°, nFo can be obtained from the following equation (2), where n is a positive integer of 1 or more.
nFo=(150×n)/L (2)
Furthermore, the characteristic impedance W of the coaxial line is expressed as follows (3), where the outer diameter of the center conductor is a, the inner diameter of the outer conductor is b, and the relative dielectric constant of the insulator between the center conductor and the outer conductor is εr. It is determined by the formula.
W=(60/√εr)×ln(b/a) (3)
Note that in equation (3), ln is a natural logarithm with base e.
When calculating the dimension ratio b/a from the above equation (3),
b/a=e ^(W/60)
From the characteristic impedance W of the lossless coaxial line 20, the ratio between the dimension a and the dimension b can be determined. Therefore, the dimensions of the outer diameter a of the center conductor and the inner diameter b of the outer conductor are set so that the characteristic impedance W is equal to the impedance Zo of Pin and Pout.

Next, let us consider a case in which a sample liquid is injected from the injection hole 12c provided in the measurement jig 1 according to the present invention shown in FIGS. 1 and 2, and the inside of the coaxial line is filled with the liquid. Since the dielectric constant εr of the liquid that serves as an insulator between the center conductor 14 and the outer conductor 12 is usually larger than 1, the length L of the coaxial line filled with the liquid is electrically n times 180°. The frequency nFs becomes nFs<nFo. That is, the wavelength of the coaxial line in the TEM mode is shortened, and the wavelength shortening rate is inversely proportional to the square root of the dielectric constant εr of the insulator between the center conductor 14 and the outer conductor 12, as shown in the following equation (4).
nFs=nFo/√εr (4)
From the above equation (4),
εr=(nFo/nFs) ² (5)
I am guided.

In the circuit shown in FIG. 3, when calculating the input impedance Zin seen from the input terminal Pin,
Zin={cosθ×Zo+j(W/Zo)sinθ}/
{j(Zo ² /W) sin θ+cos θ} (6)
becomes. In this equation (6), when θ=180°, 540°, 900°..., cosθ=-1, sinθ=0, so
Zin=Zo (7)
becomes. Also, in equation (6), when θ=360°, 720°, 1080°..., cos θ=+1, sin θ=0, so
Zin=Zo (8)
becomes. In this way, at a frequency where the phase (electrical length) of the lossless coaxial line 20 is an integral multiple of 180°, the input impedance Zin becomes the impedance Zo of Pin and Pout, regardless of the characteristic impedance W of the lossless coaxial line 20. It becomes consistent. The same applies to the output impedance Zout seen from the output terminal Pout, and the output impedance Zout comes to match the impedance Zo of Pin and Pout.

Here, in the circuit shown in FIG. 3, the frequency characteristics of the return loss RL and the insertion loss IL when the relative dielectric constant εr of the insulator between the outer conductor and the center conductor of the lossless coaxial line 20 is 25. A simulation results in the result shown in FIG. In FIG. 7, the horizontal axis represents frequencies from 0 to 1000 MHz, and the vertical axis represents insertion loss [dB] and return loss [dB]. In this case, L=0.15m and Fo=1000MHz. The wavelength shortening rate when the relative permittivity εr=25 is inversely proportional to the square root of the relative permittivity εr of the insulator, as shown in equation (4) above, so the wavelength is shortened to 1/√25=1/5. be done. That is, assuming that the dielectric constant εr of the insulator is 25, the phase of the lossless coaxial line 20 becomes 180° and matches at a frequency of 1/5 of Fo, ie, 200 MHz. This matching frequency is Fs, and referring to Figure 7, when the frequency is 200 MHz, matching becomes Fs = 200 MHz, and matching frequencies repeatedly appear on the high-frequency side, such as 400 MHz for 2 Fs, 600 MHz for 3 Fs, etc. I understand. In this way, it can be seen that although they are matched at nFs, they are mismatched at other frequencies. However, the simulation shown in FIG. 7 does not take into account the increase in insertion loss or the deterioration of return loss due to dielectric loss of the insulator of the lossless coaxial line 20.

Therefore, we will examine whether the dielectric loss of the insulator of the lossless coaxial line 20 can be replaced by adding a resistance to the circuit. In the coaxial line circuit shown in FIG. 3, a resistor R is added between the input terminal Pin and the ground, and a resistor R is added between the output terminal Pout and the ground, as shown in FIG. 4.
In the circuit shown in FIG. 4, the coaxial length of the lossless coaxial line 20 is L, its phase is θ, and the characteristic impedance is W. The outer conductor of the lossless coaxial line 20 is grounded, one end of the center conductor of the lossless coaxial line 20 is connected to the input terminal Pin, the other end of the center conductor is connected to the output terminal Pout, and the impedance of Pin and Pout is Let's say Zo. In the circuit shown in FIG. 4, the impedance of Pin and Pout is set to Zo, and the characteristic impedance W of the lossless coaxial line 20 is made equal to the impedance Zo. Here, if we limit the case to θ = 180°, θ = 180° + 360° = 540°, θ = 180° + (360° x 2) = 900°... electrically, θ = 180°. Therefore, cos θ=-1, sin θ=0, and the S parameter S21 is
S21=-1/{1+(Zo/R)} (9)
is required. Also, if we limit the case to θ=360°, θ=360°+360°=720°, θ=360°+(360°×2)=1080°... electrically, θ=360°. Therefore, cos θ = +1, sin θ = 0, and the S parameter S21 is
S21=1/{1+(Zo/R)} (10)
is required. If the insertion loss IL is calculated from S21 from equation (9) or equation (10), the same value will be obtained,
IL=20log | 1/{(1+(Zo/R)} | (11)
is required. Note that in equation (11), log is a common logarithm with a base of 10. This shows that the resistance R can replace the dielectric loss of the insulator of the lossless coaxial line 20.

By the way, the dielectric loss of a coaxial line is evenly distributed over the entire length of the coaxial line, and the lossless coaxial line 20 is expressed as microcoaxial lines CX1, CX2, CX3...CXn, If the loss is expressed by microresistances r1, r2, r3...r(2n) connected to both sides of each of the microcoaxial lines CX1 to CXn, the lossless coaxial line 20 can be expressed by the equivalent circuit shown in FIG. 5(a). be done. In the equivalent circuit shown in FIG. 5(a), the overall electrical length of the minute coaxial lines CX1 to CXn is L, its phase is θ, and the characteristic impedance is W. Ground the outer conductors of the micro coaxial lines CX1 to CXn, connect one end of the center conductor of the micro coaxial line CX1 to the input terminal Pin, connect the other end of the center conductor of the micro coaxial line CXn to the output terminal Pout, and connect the pins. Let the impedance of Pout be Zo.
Here, if we assume that the composite value of the two resistors R shown in FIG. 4 is equal to the composite resistance value of 2n micro resistors r connected in parallel,
r/2n=R/2 (12)
becomes.
In the circuit shown in FIG. 5A, the impedance of Pin and Pout is set as Zo, and the characteristic impedance W of each of the micro coaxial lines CX1 to CXn is made equal to the impedance Zo, and θ=180°. At the limit value n→∞ of n, cos(θ/n)=1, sin(θ/n)=0, and the S parameter S21 is expressed by the above equation (10). Therefore, the insertion loss IL is expressed by the above equation (11).

From this, under the conditions of FIG. 5(a) described above, the circuit of FIG. 5(a) becomes equivalent to the circuit of FIG. 5(b). In the circuit of FIG. 5(b), a resistor Rp is connected in parallel between the ground and the connection line connecting the input terminal Pin and the output terminal Pout, and the impedance of Pin and Pout is set to Zo. The resistor Rp connected in parallel is
Rp=R/2 (13)
In the circuit shown in FIG. 5(a), if the impedance of Pin and Pout is Zo, the S parameter S21 is expressed by the above equation (10), and the insertion loss IL is expressed by the above equation (11). It becomes like this. Substituting equation (13) into equation (11), we get
IL=20log | 1/{(1+(Zo/2Rp)} | (14)
is required. Since equation (14) shows the insertion loss IL in Figure 5(b), the dielectric loss of the coaxial line at frequencies where the total length of the coaxial line corresponds to a phase that is an integer multiple of 180° is It can be seen that it can be converted into a single circuit with a resistor Rp.

By the way, the coaxial line of the measuring jig 1 according to the present invention can be regarded as a concentric cylindrical capacitor Cp, and can be considered as a circuit in which a resistor Rp, which is a parasitic dielectric loss of this capacitor Cp, is connected in parallel to the capacitor Cp. considered equivalent. Therefore, an equivalent circuit of the dielectric loss tangent measuring method according to the present invention using the measuring jig 1 according to the present invention is shown in FIG. In FIG. 6, a parallel circuit of a capacitor Cp and a resistor Rp is an equivalent circuit 30 of the measurement jig 1, and a signal of a predetermined frequency is applied from a voltage source 31 to the measurement jig 1 in the equivalent circuit 30. The insertion loss IL of the equivalent circuit 30 using the measurement jig 1 can be found from the above equation (14), so if the resistance Rp is found by modifying the equation (14),
Rp={Zo×10 ^(IL/20) }/[2{1-10 ^(IL/20) }] (15)
is required. Since the characteristic impedance W is equal to the impedance Zo when the dielectric constant εr=1, substituting Zo found in the above equation (3) with W=Zo and εr=1 into this equation (15), we get
Rp={60ln(b/a)×10 ^(IL/20) }/[2{1-10 ^(IL/20) }]
= {30ln(b/a)×10 ^(IL/20) }/{1-10 ^(IL/20) } (16)
becomes.
The dielectric loss tangent tanδ in the equivalent circuit 30 is defined by the following equation (17). Note that ωn is the angular frequency of nFs (2π·nFs).
tanδ=1/(ωn×Cp×Rp) (17)

The capacitance of a coaxial line of length L of the measuring jig 1, which can be regarded as a concentric cylindrical capacitor Cp, is ε=εoεr, where ε is the dielectric constant of the insulator in the coaxial line, and the ratio of the insulator is If the permittivity is εr, the vacuum permittivity εo is a constant of 8.854×10 ⁻¹² [F/m], and the ratio of the outer diameter a of the central conductor 14 to the inner diameter b of the outer conductor 12 is b/a, then the length is The capacitance of the concentric cylindrical capacitor Cp with length L [m] can be expressed by the following equation (18).
Cp[F]=L×(2πεoεr)/ln(b/a) (18)
In formula (18), if the unit of Cp is changed from "F" to "pF",
Cp[pF]=10 ¹² × (L×2π×8.854×10 ⁻¹² ×εr)/ln(b/a)
=(55.63×εr×L)/ln(b/a) (19)
becomes.
Substituting the above equation (5), above (16) and (19) into the above equation (17) to find the dielectric loss tangent tan δ,
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) } (20)
is required. Equation (20) is the same as the above equation (1), and it can be seen that the above (1) is derived as described above. In addition, in equation (20), L is the length of the coaxial line consisting of the center conductor 14 and outer conductor 12 of the measuring jig 1 filled with liquid, and when n is a positive integer of 1 or more, nFo is This is the frequency at which the phase of the coaxial line is n times 180° when the coaxial line is not filled with liquid, and nFs is the frequency at which the phase of the coaxial line is n times 180° when the coaxial line is filled with liquid. IL is the insertion loss of the measurement jig 1 in nFs. In addition, due to the network analyzer calibration described above, the insertion loss of the measurement jig 1 when no liquid is filled in the coaxial line is standardized to 0 dB, so the IL Filling results in increased insertion loss.
As mentioned above, by determining the frequency nFs and the insertion loss IL at that time based on the measurement results of the network analyzer described above, the dielectric of the liquid filled in the coaxial line of the measurement jig 1 can be determined. The tangent tan δ can be determined from the above equation (1).

<Measurement results>
The results of measurement by the dielectric loss tangent measurement method of the present invention using the measurement jig 1 shown in FIGS. 1 and 2 according to the present invention will be explained. FIG. 8 is a chart showing the results of measurement by the dielectric loss tangent measurement method of the present invention, with the measuring jig 1 according to the present invention not filled with liquid, and is shown in Table 1.
Referring to Table 1 shown in FIG. 8, the length L of the coaxial line filled with liquid by injecting the liquid in the measuring jig 1 is 0.12 m, and the outer dimension a of the central conductor 14 constituting the coaxial line is 3.00 mm, the inner diameter dimension b of the outer conductor 12 is 7.0 mm, the dimension ratio b/a of the outer conductor 12 and the center conductor 14 is about 2.33, and the input connector 11 and the output connector 13 is a coaxial connector with a nominal value of 50Ω, and the input/output impedance Zo is 50Ω. Given the above dimensions and impedance, the frequency Fo1 at which the phase of the coaxial line corresponds to 180° (n = 1) is measured to be 1,250 MHz, and the phase of the coaxial line corresponds to 360° (n = 2). The frequency Fo2 at which the phase of the coaxial line corresponds to 540° (n = 3) is measured to be 3,750 MHz, and the phase of the coaxial line corresponds to 720° (n = 4). The frequency Fo4 is measured to be 5,000 MHz.

Next, FIG. 9 shows the frequency characteristics and return loss of insertion loss IL measured by the dielectric loss tangent measurement method of the present invention in a room temperature environment of +20° by filling the measurement jig 1 according to the present invention with pure water as a liquid. The frequency characteristics of RL are shown.
Referring to FIG. 9, the horizontal axis represents frequencies from 0 to 1000 MHz, and the vertical axis represents insertion loss [dB] and return loss [dB]. The frequency Fs1 at which the phase of the coaxial line corresponds to 180° (n=1) can be read as approximately 142 MHz, and the insertion loss IL at this time can be read as approximately 0.74 dB and the return loss RL as approximately 22.2 dB. Further, the frequency Fs2 at which the phase of the coaxial line corresponds to 360° (n=2) can be read as approximately 290 MHz, and the insertion loss IL at this time can be read as approximately 1.80 dB and the return loss RL as approximately 14.7 dB. Furthermore, the frequency Fs3 at which the phase of the coaxial line corresponds to 540° (n=3) can be read as approximately 435 MHz, and the insertion loss IL at this time can be read as 3.20 dB and the return loss RL as approximately 10.3 dB. Furthermore, the frequency Fs4 at which the phase of the coaxial line corresponds to 720° (n=4) can be read as approximately 578 MHz, and the insertion loss IL at this time can be read as 5.02 dB and the return loss RL as approximately 7.4 dB.

The dielectric loss tangent tan δ can be calculated from the above equation (20) based on the measurement results shown in FIG. 9 . In this case, the frequencies of n=1 to 4 in nFo are Fo1 to Fo4 shown in Table 1. The calculated tan δ, nFo, nFs, and insertion loss IL are measured using measurement jig 1 with input/output impedance Zo=50Ω, and the phases of the coaxial line with length L=0.12 m are 180°, 360°, 540°, A chart of numerical values at 720° is shown in FIG. 10, and Table 2 is provided.
Referring to Table 2 shown in FIG. 10, tan δ is calculated to be approximately 0.0064 at frequency Fs1 where the phase of the coaxial line is equivalent to 180° (n = 1), and the phase of the coaxial line is equivalent to 360° (n = 2 ), tan δ is calculated to be approximately 0.0084, and at frequency Fs3, where the phase of the coaxial line is equivalent to 540° (n = 3), tan δ is calculated to be approximately 0.0109, and the phase of the coaxial line is 720°. It can be seen that tan δ is calculated to be about 0.0144 at the frequency Fs4 corresponding to the angle (n=4).

In addition, in the dielectric loss tangent measurement method of the present invention, the return loss RL at nFs is also obtained as shown in FIG. 9, and the relative permittivity εr and The values of the capacitance of the capacitor Cp and the resistance Rp can be determined. From the obtained εr, Cp, and Rp, tan δ can be calculated using the above equation (17). Therefore, FIG. 11 shows a chart consisting of the return loss RL at nFs and the calculated εr, Cp, Rp, and tanδ, which is referred to as Table 3.
Referring to Table 3 shown in FIG. 11, at the frequency Fs1 where the phase of the coaxial line corresponds to 180° (n=1), the return loss RL is approximately 22.2 dB, εr is approximately 77.5, and Cp is Approximately 610.5 pF, Rp is calculated to be approximately 285.8Ω, and tan δ is calculated to be approximately 0.0064. Furthermore, at frequency Fs2 where the phase of the coaxial line corresponds to 360° (n=2), the return loss RL is approximately 14.7 dB, εr is approximately 75.4, Cp is approximately 593.7 pF, and Rp is approximately It is calculated to be 110.4Ω, and tan δ is calculated to be about 0.0084. Furthermore, at frequency Fs3 where the phase of the coaxial line corresponds to 540° (n = 3), the return loss RL is approximately 10.3 dB, εr is approximately 74.7, Cp is approximately 588.2 pF, and Rp is approximately It is calculated to be 57.1Ω, and tan δ is calculated to be about 0.0109. Furthermore, at frequency Fs4 where the phase of the coaxial line corresponds to 720° (n = 4), the return loss RL is approximately 7.4 dB, εr is approximately 74.3, Cp is approximately 585.5 pF, and Rp is It is calculated to be about 32.5Ω, and tan δ is calculated to be about 0.0144.
Here, it is known that the relative permittivity εr of pure water at room temperature and low frequency is about 80, which is found to roughly match tan δ shown in Tables 2 and 3.

From Table 2 shown in FIG. 10 and Table 3 shown in FIG. 11, based on the frequency characteristics of insertion loss IL and return loss RL shown in FIG. The frequency characteristics and relative permittivity εr were determined and shown in FIG. 12.
Referring to the frequency characteristics of tan δ shown by the solid line in FIG. 12, the horizontal axis represents the frequency from 0 to 1000 MHz, and the vertical axis represents tan δ. It can be seen that tan δ increases from a low frequency range of about 100 MHz to a high frequency range of about 900 MHz. As described above, in the dielectric loss tangent measurement method of the present invention using the measurement jig 1 according to the present invention, it is possible to obtain measurement results at high-order frequencies where n exceeds 1, and therefore, it is possible to obtain a broadband frequency characteristic of tan δ. Can be done. Furthermore, high measurement accuracy can be obtained. Further, referring to the frequency characteristics of the relative permittivity εr shown by the broken line in FIG. 12, it can be seen that the relative permittivity εr increases as the frequency becomes lower and approaches about 80 at low frequencies close to direct current.

In the dielectric loss tangent measurement method of the present invention using the measurement jig according to the embodiment of the present invention described above, the relative dielectric constant εr of the liquid filled in the measurement jig according to the present invention is determined from the wavelength shortening rate of the coaxial line. Since the conversion is performed, an accurate dielectric constant εr can be obtained. Furthermore, the measurement jig according to the present invention uses a transmission mode of a distributed constant line in which reactance components other than the resistance component, which becomes dielectric loss, disappear when the electrical length of the coaxial line is an integral multiple of the phase of 180°. It utilizes the characteristics of a certain TEM mode.
In addition, in the dielectric loss tangent measurement method of the present invention using the measurement jig of the embodiment of the present invention, the insertion loss is determined using a measuring instrument such as a network analyzer, so that the insertion loss can be obtained with high measurement accuracy. Become. Furthermore, since the return loss is accurately determined using a measuring instrument such as a network analyzer, nFs, which is determined from the return loss, can be obtained with high precision. Furthermore, since the length of the coaxial line filled with nFo and liquid can be obtained from dimensional measurements, it can be obtained with high precision, so that the relative dielectric constant εr can also be obtained accurately. Since tan δ is calculated from the calculation formula shown in equation (1) above based on these highly accurate measurement results, the accuracy of the resulting dielectric loss tangent is also high. Therefore, in the dielectric loss tangent measurement method of the present invention, tan δ can be obtained with higher accuracy than in the conventional dielectric loss tangent measurement method.
Furthermore, in the dielectric loss tangent measurement method of the present invention that uses the measurement jig of the embodiment of the present invention, it is possible to measure frequencies where the length of the coaxial line corresponds to an integral multiple of 180° by using only one measurement jig. Therefore, by integrating these measurement results, it is possible to cope with cases where wideband characteristics of tan δ are required. In this case, the length of the coaxial line filled with the liquid of the measurement jig according to the present invention can be arbitrarily selected, so that measurement can be performed in a desired frequency band.

1 Measuring jig, 11 Input connector, 11a Connector flange, 11b Screw, 12 Outer conductor, 12a Outer conductor flange, 12b Outer conductor flange, 12c Injection hole, 12d Injection hole, 12e O-ring, 12f O-ring, 13 Output connector, 13a Connector flange, 13b Screw, 14 Center conductor, 20 Lossless coaxial line, 30 Equivalent circuit, 31 Voltage source, 100 Capacitance method, 110 Voltage source, 111 Electrode, 112 Electrode, 120 Dielectric, 200 Coaxial line , 210 outer conductor, 211 center conductor, 212 connector, 213 connector, 214 screw, 215 sealing material, 220 liquid, CX1 to CXn minute coaxial line, Cp capacitor, Pin input terminal, Pout output terminal, R resistance, Rp resistance

Claims (8)

a coaxial line having a length L, which is made up of an outer conductor and a center conductor placed at the center of the outer conductor, the inside of which can be filled with a sample liquid, and an input connector provided at one end of the coaxial line; A dielectric loss tangent measurement method using a measurement jig comprising an output connector provided at the other end of the coaxial line,
Letting the impedance of the input connector and the output connector be Zo, Fo is the frequency at which the phase amount of the coaxial line in a state where no liquid is filled is 180° when a signal of a predetermined measurement frequency is input to the input connector. When the frequency at which the phase amount of the coaxial line filled with liquid is 180° is Fs, based on the insertion loss IL, Fo, Fs, and the length L of the measurement jig, nFs (n is A dielectric loss tangent measurement method, comprising calculating at least a dielectric loss tangent of the liquid at a positive integer of 1 or more. A flange having a hole capable of filling the liquid into the coaxial line is provided between the input connector and the coaxial line and between the output connector and the coaxial line, and the hole 2. The dielectric loss tangent measurement method according to claim 1, wherein after filling the coaxial line with the liquid, a screw is screwed into the hole to seal the hole. When n is a positive integer of 1 or more, the dielectric loss tangent tan δ of the liquid at nFs is:
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) }
The dielectric loss tangent measuring method according to claim 1 or 2, wherein the dielectric loss tangent can be calculated by: In addition to calculating the dielectric loss tangent of the liquid based on the insertion loss IL, Fo, Fs and the length L of the measurement jig, the calculation of the dielectric loss tangent of the liquid at nFs (n is a positive integer of 1 or more) 4. The dielectric loss tangent measurement method according to claim 1, wherein the dielectric constant is also calculated. a coaxial line having a length L, which is made up of an outer conductor and a center conductor placed at the center of the outer conductor, the inside of which can be filled with a sample liquid, and an input connector provided at one end of the coaxial line; A measurement jig comprising an output connector provided at the other end of the coaxial line,
Letting the impedance of the input connector and the output connector be Zo, Fo is the frequency at which the phase amount of the coaxial line in a state where no liquid is filled is 180° when a signal of a predetermined measurement frequency is input to the input connector. When the frequency at which the phase amount of the coaxial line filled with liquid is 180° is Fs, based on the insertion loss IL, Fo, Fs, and the length L of the measurement jig, nFs (n is A measuring jig, characterized in that it is capable of calculating at least a dielectric loss tangent of the liquid at a positive integer of 1 or more. A flange having a hole capable of filling the liquid into the coaxial line is provided between the input connector and the coaxial line and between the output connector and the coaxial line,
6. The measuring jig according to claim 5 , wherein after filling the coaxial line with the liquid from the hole, a screw is screwed into the hole to seal the hole. When n is a positive integer of 1 or more, the dielectric loss tangent tan δ of the liquid at nFs is,
tan δ=95.365×nFs×{1-10 ^(IL/20) }
/{nFo ² ×L×10 ^(IL/20) }
The measuring jig according to claim 5 or 6 , characterized in that the measurement jig can be calculated by: In addition to being able to calculate the dielectric loss tangent of the liquid based on the insertion loss IL, Fo, Fs and the length L of the measurement jig, the ratio of the liquid in nFs (n is a positive integer of 1 or more) The measuring jig according to any one of claims 5 to 7, characterized in that the dielectric constant can also be calculated.

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